DAE Problems

DAE Problems

Mathematical Specification of an DAE Problem

To define a DAE Problem, you simply need to give the function \$f\$ and the initial condition \$u₀\$ which define an ODE:

\[0 = f(du,u,p,t)\]

`f` should be specified as `f(du,u,p,t)` (or in-place as `f(resid,du,u,p,t)`). Note that we are not limited to numbers or vectors for `u₀`; one is allowed to provide `u₀` as arbitrary matrices / higher dimension tensors as well.

Problem Type

Constructors

• `DAEProblem(f::DAEFunction,du0,u0,tspan)`
• `DAEProblem{isinplace}(f,du0,u0,tspan)` : Defines the DAE with the specified functions. `isinplace` optionally sets whether the function is inplace or not. This is determined automatically, but not inferred.

For specifying Jacobians and mass matrices, see the DiffEqFunctions page.

Fields

• `f`: The function in the ODE.
• `du0`: The initial condition for the derivative.
• `u0`: The initial condition.
• `tspan`: The timespan for the problem.
• `callback`: A callback to be applied to every solver which uses the problem. Defaults to a black CallbackSet, which will have no effect.
• `differential_vars`: A logical array which declares which variables are the differential (non algebraic) vars (i.e. `du'` is in the equations for this variable). Defaults to nothing. Some solvers may require this be set if an initial condition needs to be determined.

Example Problems

Examples problems can be found in DiffEqProblemLibrary.jl.

To use a sample problem, such as `prob_dae_resrob`, you can do something like:

``````#]add DiffEqProblemLibrary
using DiffEqProblemLibrary, Sundials
prob = prob_dae_resrob
sol = solve(prob,IDA())``````